Least-Squares Image Resizing Using Finite Differences

We present an optimal spline-based algorithm for the enlargement or reduction of digital images with arbitrary (noninteger) scaling factors. This projection-based approach can be realized thanks to a new finite difference method that allows the computation of inner products with analysis functions that are B-splines of any degree n. A noteworthy property of the algorithm is that the computational complexity per pixel does not depend on the scaling factor a. For a given choice of basis functions, the results of our method are consistently better than those of the standard interpolation procedure; the present scheme achieves a reduction of artifacts such as aliasing and blocking and a significant improvement of the signal-to-noise ratio. The method can be generalized to include other classes of piecewise polynomial functions, expressed as linear combinations of B-splines and their derivatives.